The official results are due in at 7am
The UKIP leader's declaration came shortly before news agencies began projecting that the UK has voted to leave the European Union.
He said: "Dare to dream that the dawn is breaking on an independent United Kingdom.
"This, if the predictions now are right, will be a victory for real people, a victory for ordinary people, a victory for decent people.
"We have fought against the multinationals, we have fought against the merchant banks, we have fought against lies, corruption and deceit, and today honesty, decency and belief in nation, I think now, is going to win.
"We will have done it without having to fight, without a single bullet being fired, by damn hard work on the ground.
"I hope this victory brings down this failed project ... Let June 23rd go down in our history as our independence day."
Speaking to reporters Farage called on David Cameron to resign.
Meanwhile, senior Brexiteers in the Tory party have backed David Cameron to continue as Prime Minister to negotiate the UK's withdrawal.
Sterling plunged to a 31-year low on overnight markets as traders responded to growing expectations that the UK may have voted to quit the EU.
UK Shadow chancellor John McDonnell said the Bank of England may have to intervene to shore up the currency.